Problem Description
You are given an integer array nums (0-indexed). In one operation, you can choose an element of the array and increment it by 1. Return the minimum number of operations needed to make nums strictly increasing.
An array nums is strictly increasing if nums[i] < nums[i+1] for all 0 <= i < nums.length - 1. An array of length 1 is trivially strictly increasing.
Key Insights
- To make the array strictly increasing, for any element at index i, it must be greater than the element at index i-1.
- If nums[i] is not greater than nums[i-1], we need to increment nums[i] to at least nums[i-1] + 1 to maintain the strictly increasing property.
- The total number of increments needed can be tracked cumulatively as we iterate through the array.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(1)
Solution
To solve the problem, we can use a greedy approach. We iterate through the array while maintaining a variable to track the last valid number that satisfies the strictly increasing condition. For each element, if it is not greater than the last valid number, we calculate how many increments are needed and update the count of operations. The last valid number is then updated to reflect the new incremented value.